Direction ratios and direction cosines relation for JEE

Formula

\(l:m:n=a:b:c\), \quad \(l=\dfrac{a}{\sqrt{a^2+b^2+c^2}},\ m=\dfrac{b}{\sqrt{a^2+b^2+c^2}},\ n=\dfrac{c}{\sqrt{a^2+b^2+c^2}}\)

Variables: \(a,b,c\) are direction ratios; \(l,m,n\) are direction cosines.

Conditions: Not all of \(a,b,c\) are zero.

Converting DRs to DCs in spatial direction problems.